Alternating current induction motors have been developed as suitable power driving sources. Polyphase motors, including three phase motors, are widely applied in industrial and similar heavy duty applications. A rotor is rotatably mounted within an annular stator. The stator is wound with N distinct phase windings, connected to an N phase alternating current power supply, where N is an integer. The rotor is normally provided with a short circuited winding which responds to the stator field to create an induced field. An N phase power supply has phase voltages and currents which are offset from each other by 360/N electrical degrees. The N phase winding thereby develops a magnetic field which moves circumferentially about the stator and rotor. The induced field tends to align with and follow the rotating field to create a rotating force and motion of the rotor as a result of the electromagnetic coupling between the fields of the stator and the rotor.
An alternating current motor is commonly driven by an inverter. An inverter is a device capable of supplying alternating current of variable voltage and variable frequency to the alternating current motor, allowing for control of machine synchronous speed and thus of machine speed. The inverter may also be used with alternating current generators, and can cause an alternating current motor to act as a generator for braking applications. An alternating current motor may be an induction motor, a synchronous motor with either a wound rotor or permanent magnet rotor, or a brushless DC motor.
In many cases, the cost of the inverter is considerably greater than the cost of the motor being supplied. It is thus necessary to minimize the size of the inverter power electronics in order to control system cost.
Whereas the alternating current machine itself may have substantial overload capability, and may carry currents of the order of five to ten times full rated current for periods measured in minutes, the overload capability of the inverter electronics is severely limited. Exceeding the voltage or current ratings of the inverter electronics will swiftly cause device failure. Commonly, inverter electronics is specified such that it can tolerate 150% of nominal full load current for 1 minute, and for any given motor, and inverter will be selected which has the same nominal current capability as that of the motor.
Voltage is set internally by the inverter system or by the rectified supply voltage. Voltage overload is normally not specified, and will cause near instantaneous destruction of semiconductor elements. The voltage ratings of the semiconductors instead set the maximum output voltage of the inverter system, and an inverter will be selected which has a maximum output voltage that matches the operating voltage of the motor at full speed.
With any reasonably sized inverter, substantial motor overload capabilities remain untapped.
Electrical rotating machinery presents an impedance characteristic that varies according to mechanical load and rotational velocity. As the speed of the electrical rotating machine is increased, the voltage produced by a generator, or the voltage required by a motor will tend to increase proportionally. For example, in an induction motor, in order to maintain a constant magnetic field strength as the applied frequency is changed, a constant ratio of applied voltage to frequency is maintained. For permanent magnet machines, the back-EMF produced by the motor will increase as rotor speed increases, again requiring increased voltage in order to drive the machine. U.S. Pat. No. 6,812,661 to Maslov discloses changing motor topology on a dynamic basis to obtain maximum efficiency for each of a plurality of operating speed ranges. A plurality of mutually exclusive speed ranges between startup and a maximum speed at which a motor can be expected to operate are identified and a different number of the motor stator winding coils that are to be energized are designated for each speed range. The number of energized coils is changed dynamically when the speed crosses a threshold between adjacent speed ranges. Even direct current machines (not covered by the present invention) require increased voltage as speed is increased, if magnetic field strength is maintained as a constant.
In general, the required voltage is expressed in terms of Volts/Hertz.
For traction application, there is often only limited available electrical power. Thus requirements for high overload capability can only be met at low speed, where high torque is required for starting, but reduced speed means that mechanical power output is still low. Such low speed torque requirements require high current to flow though the motor, but do not require high operating voltage. It is thus possible to trade high speed operating capability for low speed overload capability at the design stage of a motor drive system.
By increasing the number of series turns in the motor windings, higher slot current may be achieved with the same terminal current, thus permitting the same inverter to provide greater overload current to the motor. This increase in overload capability comes at a substantial cost. The increased number of series turns means that the motor operating voltage is increased, operation at high speed is prevented. Most motors are designed for dual voltage operation, through the expedient of operating various sub-circuits of the motor in series or parallel connection. The change between series and parallel connection may be accomplished though suitable contactor arrangements, permitting the motor to be operated with a higher number of series turns at low speed, and a lower number of series turns at high speed. For a simple three phase alternating current machine system, such a system would require at least two single-pole three-phase contactors, and would only offer a factor of 1.7 increase in low speed overload capability. With three contactors, a factor of two change is possible.
The change in series turns may be considered a change in alternating current machine impedance, or current versus voltage relation. Normally, an alternating current machine will have a fixed relationship between synchronous speed and impedance, characterized by the Volts/Hertz ratio. For a given inverter and machine frame, a machine wound with a higher Volts/Hertz ratio will have a lower maximum speed, but higher peak low speed torque.
It is thus highly desirable to provide an alternating current machine drive system in which the alternating current machine presents a variable Volts/Hertz ratio to the inverter. For high speed operation, the Volts/Hertz ratio would be adjusted to a low value, in order to maintain a suitable alternating current machine operational voltage. For low speed operation, the Volts/Hertz ratio would be adjusted to a higher value, so as to permit high overload torque operation.
In this disclosure, many of the following abbreviations are used:
RD: rotational degrees on the stator
ED: electrical degrees
H: harmonic order
P: pitch factor
B: base pole count, i.e. number of magnetic poles developed by a machine driven by fundamental frequency, H=1.
Kc: chording factor
N: number of different driven electrical phases in a machine
F: phase angle of any given winding phase
Δ: phase angle difference of the inverter output phases driving the windings
L: spanning value of mesh connection
V: volts
Vw: Voltage across a winding
Vout: output to neutral voltage of the inverter
W: Winding phase number
S: Slot number
T: Turn count
The term ‘winding’ herein refers to the group of all of the windings and/or coils and/or conductors of a single phase, unless otherwise specified. In a conventionally wound induction machine, the winding that constitutes each phase consists of a ‘supply half’ and a ‘back half’. The current flow from the ‘supply half’ is in the direction as it is supplied by the power supply The phase angle of the back half of each phase is equal to the phase angle of the supply half, offset by 180 ED. The windings are wound of copper or other low resistance wire or other conductors.
The following equations are also used, and presume even winding distribution. The same principles apply, with slightly more complicated mathematics, even if the winding distribution is not even:
F = 360*H*W/N(i)Vw = 2*sin((B*H*Δ)/4)*Vout(ii)P = (winding pitch in RD)*H*B/360(iii)Kc = sin(90*P)(iv)
An inverter is a device capable of supplying alternating current of variable voltage and variable frequency to the alternating current machine, allowing for control of machine synchronous speed and thus of machine speed. The inverter may also be used with alternating current generators, and can cause an alternating current motor to act as a generator for braking applications. An alternating current motor may be an induction motor, a synchronous motor with either a wound rotor or permanent magnet rotor, or a brushless DC motor.
Background—Mesh Connected Machines
In my previous patents and applications, incorporated herein by reference, there have been disclosed details of high torque compact motors that may be used in conjunction with the present invention. In U.S. Pat. No. 6,922,037, the use of high phase order machines are described, in which induction machines are equipped with more than three different phases. These increase the useful available torque. In U.S. Pat. No. 6,838,791, the use of connecting a high phase order machine with a mesh connection is described. A benefit of this is that by varying between harmonic drive frequencies of a mesh connected machine, the impedance of the machine may be dramatically changed. In WO2006002207, the benefit of using a short pitch winding with a mesh connected high phase order machine is disclosed. A benefit of this is that even order harmonic drives maybe utilized.
A mesh connected windings machine is disclosed in my previous abovementioned patents and applications. The mesh connection may be defined as follows. Each of N windings is connected between two of N inverter outputs. A first terminal of each winding phase is connected in phase angle order to one of the N inverter outputs. A phase angle difference is produced by connecting the second terminal of each winding to a second inverter phase. Δ represents the phase angle difference between the inverter output phases across the two terminals of each winding. All of the windings in a machine have the same value of Δ. Δ is measured according to H=1 and is irrespective of the harmonic order of the drive waveform. A low Δ is produced by connecting the first terminal of a winding to a first inverter phase, and the second terminal of the winding to the next inverter phase. For example, in a 9 phase machine, Δ may be 40, 80, 120 and 160 ED.
A preferred embodiment of a mesh connected machine is a high phase order machine in which each phase terminal is separately connected to an inverter output. The windings of the induction machine are wound with the motor terminals connected in a mesh connection to produce a low impedance output. The inverter is capable of operating with a variable phase sequence that changes the effective impedance of the motor.
In a mesh connected machine, the voltage applied to a given winding, which is measured from one terminal of the winding to the other terminal of the winding, will in general be different from the phase to neutral voltage fed to the machine. The reason for this is that the supply will be from a machine of different connection, and thus the relevant voltage measurements will give different results. Specific identified phase-to-phase voltages will always be the same for two connected high phase order machines, however the voltage placed across a winding or switching element will likely be different.
The following equations relate the voltage placed across the windings of a mesh connected machine to the voltages applied to the machine terminals as measured between the terminal and neutral. These are the equations which relate the output voltages of a star connected supply to the winding voltages of a mesh connected motor, and can be inverted to relate a mesh connected supply to a star connected motor. The equations could be used twice to describe a mesh connected supply connected to a mesh connected motor.
                              V          K                =                              V            MAX                    ⁢          Re          ⁢                      {                          ⅇ                              ⅈ                ⁢                                                                  ⁢                                  h                  ⁡                                      (                                                                  ω                        ⁢                                                                                                  ⁢                        t                                            +                                                                                                    2                            ⁢                            K                                                    m                                                ⁢                        π                                                              )                                                                        }                                              (        1        )            
Equation 1 describes the line to neutral voltage of the supply, where m is the number of phases in a balanced supply, K is the particular phase of interest, and may range from 0 to m−1, ω is the frequency of the alternating current in radians per unit time, t is time, h is the harmonic order being generated, and VMAX is the peak voltage of the output waveform. The equation is written using standard complex exponentiation form, in which the constant e is raised to a complex number. In this case, the exponent is a purely imaginary value, thus the result of the exponentiation has constant periodicity over time. Only the real portion of this periodic function is used.
The terms in the exponent include a function of time, which results in the periodic nature of the voltage with time, and a constant rotation term, which results in the phase difference between the various phases.
Rearranging Equation 1, clearly separating the constant and periodic terms, gives:
                              V          K                =                  Re          (                                    V              MAX                        ⁢                          ⅇ                              ⅈ                ⁢                                                                  ⁢                h                ⁢                                                                  ⁢                ω                ⁢                                                                  ⁢                t                                      ⁢                          ⅇ                              ⅈ                ⁢                                                                  ⁢                                                      2                    ⁢                                                                                  ⁢                    hK                                    m                                ⁢                π                                              )                                    (        2        )            
It is clearly seen that each phase differs from the other phases only by the constant rotation term, and that the periodic term does not depend in any way upon the particular phase.
The voltage across the particular winding K as a function of the voltage applied to its two ends is given by Equation 3.VWK=VK−V(K+L) % m  (3)
The voltages applied to winding K are simply that of phase K and phase K+L, where L is the spanning value for the particular mesh connection, which represents the number of inverter output phases between the first and second terminal of each single phase winding. The greater the spanning value, the greater the voltage placed upon a winding for a given inverter output voltage. Expanding Equation 3 using the terms in Equation 2 gives:
                    =                              Re            (                                          V                MAX                            ⁢                              ⅇ                                  ⅈ                  ⁢                                                                          ⁢                  h                  ⁢                                                                          ⁢                  ω                  ⁢                                                                          ⁢                  t                                            ⁢                              ⅇ                                  ⅈ                  ⁢                                                                          ⁢                                                            2                      ⁢                      hK                                        m                                    ⁢                  π                                                      )                    -                      Re            (                                          V                MAX                            ⁢                              ⅇ                                  ⅈ                  ⁢                                                                          ⁢                  h                  ⁢                                                                          ⁢                  ω                  ⁢                                                                          ⁢                  t                                            ⁢                              ⅇ                                  ⅈ                  ⁢                                                                          ⁢                                                            2                      ⁢                      h                      ⁢                                              (                                                  K                          +                          L                                                )                                                              m                                    ⁢                  π                                                      )                                              (        4        )            
Equation 4 may be rearranged as follows:
                    =                  Re          (                                    V              MAX                        ⁢                                          ⅇ                                  ⅈ                  ⁢                                                                          ⁢                  h                  ⁢                                                                          ⁢                  ω                  ⁢                                                                          ⁢                  t                                            ⁡                              (                                                      ⅇ                                          ⅈ                      ⁢                                                                                          ⁢                                                                        2                          ⁢                          hK                                                m                                            ⁢                      π                                                        -                                      ⅇ                                          ⅈ                      ⁢                                                                                          ⁢                                                                        2                          ⁢                          h                          ⁢                                                      (                                                          K                              +                              L                                                        )                                                                          m                                            ⁢                      π                                                                      )                                              )                                    (        5        )                                =                  Re          ⁡                      (                                          V                MAX                            ⁢                                                ⅇ                                      ⅈ                    ⁢                                                                                  ⁢                    h                    ⁢                                                                                  ⁢                    ω                    ⁢                                                                                  ⁢                    t                                                  ⁡                                  (                                                            ⅇ                                              ⅈ                        ⁢                                                                                                  ⁢                                                                              2                            ⁢                            hK                                                    m                                                ⁢                        π                                                              -                                                                  ⅇ                                                  i                          ⁢                                                                                                          ⁢                                                                                    2                              ⁢                              hK                                                        m                                                    ⁢                          π                                                                    ⁢                                              ⅇ                                                  ⅈ                          ⁢                                                                                                          ⁢                                                                                    2                              ⁢                              hL                                                        m                                                    ⁢                          π                                                                                                      )                                                      )                                              (        6        )                                =                  Re          ⁡                      (                                                            V                  MAX                                ⁡                                  (                                      1                    -                                          ⅇ                                              ⅈ                        ⁢                                                                                                  ⁢                                                                              2                            ⁢                            hL                                                    m                                                ⁢                        π                                                                              )                                            ⁢                              ⅇ                                  ⅈ                  ⁢                                                                          ⁢                  h                  ⁢                                                                          ⁢                  ω                  ⁢                                                                          ⁢                  t                                            ⁢                              ⅇ                                  ⅈ                  ⁢                                                                          ⁢                                                            2                      ⁢                      hK                                        m                                    ⁢                  π                                                      )                                              (        7        )            
Equation 7 is the desired result, separating the exponential term into constant and periodic portions of the various variables. Of particular interest is that the term VMAX, the periodic term, and the constant rotation term all remain as in the original equation, but an additional term is added. This term depends upon the applied harmonic h, the spanning value L, the number of phases m, but is independent of the particular phase K and is also independent of frequency ω or time t.
Equation 7 shows that the voltage applied to a winding depends upon the voltage output of the supply, but it also depends upon the harmonic order h and the spanning value L. By changing the spanning value, as for example by connecting the machine using a different mesh connection, the voltage applied to the winding will change even if the voltage output of the supply remains constant.
These equations demonstrate that for a given machine, the Volts/Hz ratio of the machine may be changed by altering either the harmonic applied by the inverter to the mesh connection, or by altering the spanning value L of the mesh connection between the inverter and the rotating machine.
The advantage of changing the harmonic applied by the inverter to the mesh connection is that the change in Volts/Hz ratio may be obtained through a logical change of the output synthesized by the inverter. This means that the motor may have a fixed electrical connection to the inverter. This technique is disclosed in my U.S. Pat. No. 6,657,334.
Furthermore, if desired, the change in harmonic content may be obtained in a smooth fashion, successively passing through various admixtures of harmonic components. Thus there need be no sudden discontinuity in drive when switching between harmonic operating states. Disadvantages of this technique are that it requires a machine capable of operation with harmonic drive; e.g. a pole count changing alternating current machine, or a synchronous machine with variable pole count rotor, or a permanent magnet machine with a rotor which reacts both to the fundamental and the harmonic components of the drive waveform. An additional disadvantage with a pole count changing alternating current machine is that the basic efficiency of such a machine will go down as the pole area is reduced. However the elimination of mechanical contactors is a benefit.
The advantage of changing the spanning value L is that the same machine pole count is maintained. Thus methods that change the spanning value L are applicable to machines with fixed pole counts. This includes some wound rotor alternating current machines, as well as most synchronous machines, permanent magnet machines, and brushless DC machines. Furthermore, for alternating current machine operation, pole area is maintained, which increases machine efficiency. Finally, changing the spanning value L generally permits a greater number of possible Volts/Hz ratios to be obtained from the same machine. Disadvantages of changing the spanning value L are that a mechanical contactor arrangement must be used to physically change the electrical connectivity of the mesh connection, and that power to the motor must be interrupted in order to change the mesh connection.
In a rotating electrical machine, each phase winding set can be described by two terminals. There may be a larger number of terminals, but these are always grouped in series or parallel groups, and the entire set can be characterized by two terminals. In a star connected machine, one of these terminals is driven by the inverter or power supply, while the other terminal is connected to the machine neutral point. All current flows through one terminal, through the neutral point into other windings, and though the driven terminals of the other phases. In a mesh-connected machine, these two terminals are connected directly to two different supply points.
An example of how this may be done is shown in FIG. 1a, in which stator slots 4 are shown as straight lines running down the inside of the stator, and inverter output phases 2, are shown as circles, alongside which is marked phase angles of each of the inverter output phases. Electrical connections 3 between the winding terminals in stator slots 4 and inverter output phases 2 are represented by dashed lines. Two winding halves are displayed opposite one another, and are actually joined to one another, although this is not shown. The configuration describes a 9 phase machine connected with an L=4 connection, as shown in FIG. 1d. 
In contrast to three phase systems, in which there are only three inverter output phases and six motor windings terminals, in a high phase count system with N phases, there are N inverter output phases and 2N motor windings terminals. There are thus a substantial number of choices for how an N phase system may be mesh connected. This set of choices is greatly reduced by rotational symmetry requirements, specifically each winding must be connected to two inverter output phases with the same electrical angle difference between them as for every other winding.
A simple graphical schematic of the permissible inverter to motor windings connections may thus be described for a polyphase motor having N phases. In the following embodiment, N is equal to 9, but it is to be understood that this limitation is made to better illustrate the invention; other values for N are also considered to be within the scope of the present invention. FIG. 1b shows 9 evenly spaced terminals 4 and a center terminal 6. Each of the terminals 4 represent one end of a motor winding 1 and the center terminal 6 represents the other end of the motor winding. An inverter 5 has 9 inverter output phases 2, which are connected to one of the terminals 4 of each of the motor windings 1 via electrical connectors 3 as shown.
Permissible connections of the 9 phase windings are either from the center point, to each of the 9 points on the circle (this being the star connection shown as FIG. 1a) or from each of the 9 points to another point. This latter is shown in FIG. 1d; in FIG. 1c motor winding 1 is represented by a line, and in FIG. 1d inverter 5 and electrical connectors 3 have been omitted for the sake of clarity. It will be noted that for each L from 1 to 4 there is a corresponding L from 5 to 8 that produces a mirror image connection.
FIG. 1d shows all permissible connections for a 9 phase system from L=1 to L=4 as well as the star connection. Noted on the star connection diagram are the relative phase angles of the inverter phases driving each terminal. For a given inverter output voltage, measured between an output terminal and the neutral point, each of these possible connections will place a different voltage on the connected windings. For the star connection, the voltage across the connected windings is exactly equal to the inverter output voltage. However, for each of the other connections, the voltage across a winding is given by the vector difference in voltage of the two inverter output phases to which the winding is connected. When this phase difference is large, then the voltage across the winding will be large, and when this phase difference is small, then the voltage across the winding will be small. It should be noted that the inverter output voltage stays exactly the same in all these cases, just that the voltage difference across a given winding will change with different connection spans. The equation for the voltage across a winding is given by:
  2  ⁢      sin    ⁡          (              Δ        2            )        ⁢      V    out  where Δ is the phase angle difference of the inverter output phases driving the winding, and Vout is the output to neutral voltage of the inverter.
Thus, referring to FIG. 1c, when L=1, the phase angle difference is 40 degrees, and the voltage across a winding is 0.684 Vout. When L=2, the phase angle difference is 80 degrees, and the voltage across the winding is 1.29 Vout. When L=3, the phase angle difference is 120 degrees, and the voltage across the winding is 1.73 Vout. Finally, when L=4, the phase angle difference is 160 degrees, and the voltage across the winding is 1.97 Vout. For the same inverter output voltage, different connections place different voltage across the windings, and will cause different currents to flow in the windings. The different mesh connections cause the motor to present different impedance to the inverter. In other words, the different mesh connections allow the motor to use the power supplied by the inverter in different rations of voltage and current, some ratios being beneficial to maximize the torque output (at the expense of available speed), and some ratios to maximize the speed output (at the expense of maximum available torque).
As shown in FIG. 1c, the inverter outputs may be represented as points on a unit circle, with the relative positions of the points representing the phase angle of this inverter output. The winding of the motor is composed of individual single phase windings, each of which as two terminals. The single phase windings are represented by line segments, and are the single phase sub-elements described above. The end points of these line segments represent the terminals of the windings. When one terminal of each winding is connected to the origin, and the other terminal is connected to an inverter output as represented by a point on the unit circle, then a star connection may be represented. When line segments are connected between points on the unit circle, then a mesh connection is represented. An M phase symmetrical mesh connection will be represented by a diagram which has M fold rotational symmetry.
Each of the mesh connections may be represented by the spanning value ‘L’, which represents the number of inverter output phases between the first and second terminal of each single phase winding. The greater the spanning value, the greater the voltage placed upon a winding for a given inverter output voltage. Changes in spanning value may be considered a rotation of the connection between second terminals of each single phase winding and the inverter output phases.
In the foregoing and my previous patents, U.S. Pat. Nos. 6,657,334, 6,831,430, and 6,838,791, I disclosed details of high phase order induction machines. I focused particularly upon concentrated, full pitch windings, and the use of odd order harmonics. A benefit of these machines is that odd order harmonics with a harmonic number up to the phase count are marshaled to produce only beneficial torque. For the purpose of this disclosure as well as my previous disclosures, the term ‘harmonic’ was used to identify power supply phase angle relationships which were associated with the phase angles of harmonics in a fundamental drive frequency. The ‘pure’ harmonic is used as a new drive waveform, and results in a change in the number of magnetic poles developed by the motor. Harmonic drive may also be described as a multiplicative change in the power supply phase angles used to drive each winding. In this description, ‘H’ refers to the order of the harmonic drive. For example, H=1 refers to first harmonic drive, or fundamental drive waveform. H=2 refers to second harmonic drive, H=3 is third harmonic drive, etc. H=1 is not limited to any particular frequency, such as 50 Hz, and may instead be variable. However, in order to preserve clarity in the present disclosure, H=1 is mentioned as if it were a fixed frequency.
A machine is wound to give a base number of poles, B, which is the number of poles that are developed with fundamental harmonic drive (H=1). When a harmonic drive is used, the number of poles developed is equal to B*H, for example, if B=2, H=1 develops 2 poles, H=3 develops 6 poles, etc.
Full pitch windings (180 RD between supply and back windings) make most efficient use of the conductors in the slots. Concentrated windings permit maximum harmonics tolerance. With a lap winding, even order values of H are not useable with full pitch windings because of symmetry requirements. If even order values of H are applied to a full pitch winding, a ‘magnetic short circuit’ results, in which current flowing through the back half of the winding is in near opposition to the current in the supply half of the winding. The counter-flow currents cancel each other out, no magnetic field is produced, and machine inductance drops.
The lower the pole count, the more efficiently the machine operates. However, for various reasons, higher order pole count operation is often used, for example, for high torque applications. Nevertheless increasing the pole count unnecessarily, results in inefficiency. As mentioned, the drive harmonic impedance effect enables large changes in impedance simply by switching between two different drive harmonics, each associated with a different impedance characteristic. However, since the impedance effect depends on switching between two harmonics, the pole count may become unnecessarily high if only odd order drive harmonics are usable. In WO2006002207, I described a machine that can also be driven with even order harmonics. As may be seen from equation (iii), the pitch factor for the windings depends on both the harmonic order, and the winding pitch of the windings, measured in rotational degrees on the stator. Thus a winding pitch may be selected for the windings to result in a pitch factor that is not zero for each required harmonic drive. Full pitch windings, in which each winding spans 180 RD, produce a pitch factor of zero for all even order harmonics. Shorter or longer pitch windings are able to tolerate even order harmonic drive.
An example of a short pitch winding is shown in FIG. 2. Referring now to FIG. 2, a winding schematic is provided of a 36 slot, 36 phase machine with a short pitch winding. The design not limited to any particular number of slots or phases, and the example is given for exemplary purposes only. Stator slots are numbered 1-36. The lines adjacent the slots each represent the winding in that slot. The 36 windings are numbered W0-W35, only a few of which are marked, for clarity. Each winding is a different driven phase. The bend in each winding on the diagram represents the stator end turn and renders each winding as two halves, a supply half and a back half. The back half always has a phase angle difference of 180 ED from the supply half. Each winding has a pitch of 1:13, which represents a short pitch winding and the base number of poles, B, is 2. The slots containing the supply half and the back half of each phase are 120 RD apart from one another on the stator. The windings are concentrated, meaning that each half winding is not distributed over more than one slot. An N phase power supply supplies N voltages and currents to provide each winding with an electrical phase.
In the present example, each slot contains two winding halves. For example, winding W0 goes through slot 1 and returns via an end turn in the reverse direction through slot 13. Similarly, winding W2 goes in one direction through slot 2 and in the reverse direction through slot 14. In slot 13 is one half of winding W12, the other half of which is located in slot 25. According to equation (i) for H=1: W0 in slot 1 is driven with 0 ED, the other half of W0, in slot 13, is driven with 180 ED, and W12 in slot 13 is driven with 120 ED.
This shows that the two winding halves in any slot are 60 ED out of phase from one another. They are enough in phase to produce a reasonably combined slot current at 150 ED. However, since the different winding halves occupying each slot are somewhat out of phase, the effective slot current is something less than the sum of the two half currents, resulting in higher voltage and lower current. The efficiency of magnetic field production is reduced, but remains acceptable. The degree to which the voltage/current ratio is increased is measured by the aforementioned chording factor, Kc, applied to the turn count of the winding. The Kc of a high phase order machine with variable harmonic drive may be determined according to equation (iv).
When a winding is full pitch, the Kc for all odd order harmonics is 1, and the Kc for all even order harmonics is 0. A harmonic order that produces a Kc of zero is unable to drive the machine. Therefore, only odd order harmonics can drive a full pitch wound machine. However, in any short pitch winding machine, each harmonic order may produce a different Kc, dependent on the actual winding pitch.
In the machine of FIG. 2, the pitch is 0.67 for H=1, 1.33 for H=2, 2 for H=3, 2.67 for H=4, and 3.33 for H=5. H=1, H=2, H=4 and H=5 all produce a Kc of 0.87, and are therefore able to drive the machine. However, in the same machine, H=3 has a Kc of 0, so is prohibited.
In a mesh connected machine, Vw depends on the values of Δ and H. The V/Hertz ratio of the machine is dependent on Vw. It is also well known that the speed/torque output of the machine is dependent on the turn count, T, multiplied by the Kc. A novel feature of the present design is that not only are even order harmonics allowed, but the short pitch high phase order machine also presents a variable Kc, dependent upon both the pitch factor P, and the harmonic order.
The lower the Kc is, the higher the machine speed/torque ratio. In a mesh connected machine, it is possible to identify different operating regimes, such as high torque operation, or high speed operation. Each regime may be assigned a different harmonic order, identified to produce a V/Hertz ratio most suited to the regime. Table 1 gives recommendations as to the speed/torque relation associated with different values of H, Δ and Kc. In addition, as mentioned above, certain values of Δ give the greatest range in Vw under operation with different harmonics.
For example, when Δ is close to 120 ED, a large range in V/Hertz is produced between H=1 and H=3, in which H=1 produces a low V/Hertz ratio, while H=3 produces a high V/Hertz ratio. Therefore, H=3 is suited to low speed, high torque operation, since it allows the maximum torque to be produced. H=1 would be suited to high speed operation since it allows maximum speed to be produced. Since H may be varied electronically, a variable percentage of each harmonic may be applied at once, superimposed upon one another. The operating regimes may have a great deal of overlap, and a V/Hertz ratio may be optimized for an application's need in real time.
The Kc is also dependent on H, and the winding pitch must be chosen at the design stage to have desirable characteristics with regard to the regimes in which each harmonic is likely to be used.
If an application requires that a very high torque be produced at low speeds, and yet high speeds should not be compromised, a solution is as follows: At least two harmonics are identified, one to produce a low V/Hertz ratio and one to produce a high V/Hertz ratio. A winding pitch should be chosen that has a low Kc for the harmonic with a low V/Hertz ratio. This ensures that the top speed of the high speed operating regime will not be compromised. At the same time, the winding pitch should have a high Kc for the harmonic that produces a high V/Hertz ratio. The high Kc enables a low speed/torque ratio—and thus an effective torque boost—in the low speed, high torque operating regime. In the above example (in which B=2, and F is close to 120 ED, and H=1 is suited for high speed operation, and H=3 is suited for high torque operation), a very short pitch winding such as 60 RD will provide H=1 with a Kc of 0.5 and H=3 with a Kc of 1. The high speed/torque relation of H=1 is maintained, and the low speed/torque relation of H=3 is further decreased. If the identified harmonics were H=1 and H=2, the pitch would be chosen to be close but not equal to 90 RD.
However, other applications may have other requirements, and therefore each harmonic order should be matched with a Kc that meets the requirements of the application. For example, another application may require high torque at all speeds even at the expense of reaching top speeds. Therefore, a high Kc should be provided for each of the harmonic orders to be used.
Background—Motor Topographies
Common motors nowadays are cylindrically shaped. However, pancake motors are sometimes also used.
U.S. Pat. No. 6,892,439 to Neal, et al, is directed to a motor including a stator having multiple conductors that create a plurality of magnetic fields when electrical current is conducted through the conductors. The stator has a pair of opposing end surfaces in contact with each other forming a toroidal core. A monolithic body of phase change material substantially encapsulates the conductors and holds the toroidal core in place. The stator is formed by laminating strips together to form a linear core preform, winding wire around poles extending from a side of the core preform, then rolling the preform to bring its two ends together to form the toroidal core. Hard disc drives using the motor, and methods of constructing the motor and hard disc drives are also disclosed.
Some of the earliest motors were toroidal wound, including some of Tesla's work. For example, U.S. Pat. No. 382,279 to Tesla is directed to a toroidal motor.